The advancement of reaction and separation technologies requires the ongoing development of porous materials. For example, the development of porous carbons having high porosity has led to their wide use in industrial applications such as catalysis, capacitor electrodes, adsorptive gas separations and gas storage. In addition, in applications such as optics and shape selective catalysis, where the ordering of a porous material is important, aluminosilicate structures are of special interest.
It is appreciated that engineering new porous materials requires knowledge on the textural properties and their relationship to the performance of the material. Furthermore, it is known that pore volume and surface area are properties indicative of the capacity of a given porous material. Pore size distribution (PSD) is also useful since it is sensitive to pore size, geometry and pore connectivity.
Porosimetry, i.e. the characterization of porous materials using gas adsorption, is a well-known technique. Typically, pore size distribution of a sample is determined by dosing gas into the pores. The measured gas uptake is used to interpret the frequency of pore size at a corresponding pressure, along with micro, meso and total pore volume, plus surface area of the sample. Porosimetry with N2 and Ar is conducted at cryogenic temperatures to keep the adsorption pressures below atmospheric. This eases some instrumental requirements as high pressures are not required, however, such low temperatures slow down adsorption rates inside microporous materials such that true equilibrium of the gas uptake is not achieved. With this in mind CO2 adsorption measurements at 273 K have been used for micropore characterization. Thus, as of today, the most prevalent method to characterize the micro, meso and macro pores of a material is to use N2 adsorption isotherm for meso and macro pores and then CO2 adsorption for the micropores. The pore size distribution can then be determined from an adsorption isotherm using appropriate models.
It is appreciated that different molecules can give different information regarding a given sample pore structure and pore connectivity due to a molecule's inherent size and polarizability, and its interactions with pore size and surface chemistry of the adsorbent. Moreover, characterization models usually assume pore walls to be smooth with no chemical heterogeneity. However, in most cases this is not an accurate assumption and can thus result in errors in the pore size distribution calculations. In addition, the use of two different probe molecules can introduce different degrees of uncertainty for micro and mesopore regions.
Regarding adsorption techniques, adsorption measurements are mostly conducted using volumetric or gravimetric instruments. Volumetric instruments typically have a relatively simple design and operate based on pressure changes during gas adsorption on the adsorbent in a known confined volume. Also, adsorption analysis using volumetric instruments is typically employed for adsorption measurements using light gases near room temperature.
Gravimetric instruments measure gas uptake using magnetic micro-balances. This method is less accurate for small quantities of uptake of light gases like H2. However, gravimetric instruments use an uptake measurement sensor that is separated from a pressure transmitter and thus pressure can be altered independently while collecting adsorption data.
Not being bound by theory, adsorption of a gas on an adsorbent in a confined volume reduces the gas pressure. Therefore, gas can be injected at controlled flow rates into the adsorption chamber in order to maintain a constant pressure. It addition, the effect of pressure changes on gas uptake rates depends on the rates of surface adsorption and molecular diffusion dynamics for a given the adsorbent-adsorbate system.
A kinetic approach to an adsorption process can be treated as a collection of elementary steps where each step is a linear function of the adsorption driving force (e.g. pressure of more chemical potential). In the alternative, pseudo-first and pseudo-second order kinetic models are used to describe adsorption dynamics since they can fit on a large variety of adsorption processes. They are special cases of a more general expression, Langmuirian adsorption kinetics. Taking the kinetics approach to the Langmuir isotherm the following expressions can be written as:ra=kaP(θe−θ)  (1a)rd=kdθ  (1b)where ra and rd are the adsorption and desorption rates, respectively, ka and kd are the adsorption and desorption rate constants, respectively, θ is the surface coverage, θe, is the equilibrium coverage at each measurement condition, and P is the gas pressure. By subtracting these two terms the net rate of adsorption can be obtained as:dθ/dt=kaP(θe−θ)−kdθ  (2)
While the rate constants, ka and kd are typically functions of temperature, but not pressure, when the adsorption measurements are made under isothermal and isobaric conditions, they remain constant. Hence, the adsorption rate is a first order function of the concentration (chemical potential) gradient.
Aside from pressure and temperature effects, the nature of adsorbent porosity plays the dominant role in determining gas adsorption dynamics. In particular, gas uptake is associated with micropore filling, monolayer completion in micropores, and capillary condensation inside mesopores. In addition, when adsorption equilibrium data are collected at moderate to high resolution, i.e. during small changes in pressure, the adsorption dynamics can be expressed as a function of pressure.
Conventional adsorption instruments dose the adsorbate gas into the system and then allow no disturbances until the local equilibrium (or pseudo-equilibrium) point is reached. However, such a condition can and often does take a very long time to reach when using nitrogen at 77K. As such, an improved process for characterizing micro and mesoporous materials would be desirable.